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complex-numbers/README.md

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Create and activate a virtual environment:
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```shell
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$ python -m venv venv
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$ python -m venv ./venv
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$ source venv/bin/activate
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```
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Install dependencies into your active environment:
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```python
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(venv)$ python -m pip install -U pip jupyterlab ipywidgets matplotlib pillow
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(venv)$ python -m pip install -U pip jupyterlab ipywidgets matplotlib
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(venv)$ python -m jupyter labextension install @jupyter-widgets/jupyterlab-manager
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```
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complex-numbers/bermuda.ipynb

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"source": [
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"## Flipping\n",
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"\n",
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"To flip a complex number around an axis, **negate** the relevant component or calculate the **complex conjugate** for the vertical symmetry:"
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"To flip a complex number around an axis, take the **negative** of the relevant component or calculate the **complex conjugate** for the vertical symmetry:"
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complex-numbers/fourier.ipynb

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"source": [
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"## Mixing Tones\n",
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"\n",
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"Let's mix a few sine waves to produce a sound comprised of multiple frequencies. If you choose close frequency values, then you'll hear a peculiar [beating](https://en.wikipedia.org/wiki/Beat_(acoustics)) interference pattern:"
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"Let's mix a few sine waves to produce a sound comprised of multiple frequencies."
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]
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},
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{
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"cell_type": "markdown",
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"id": "55a3c27c-acdf-4a96-bcc6-0613ac2068aa",
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"metadata": {},
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"source": [
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"<div class=\"alert alert-warning\">\n",
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" <strong>Note:</strong> The function below declares a variable as global, which is usually considered a bad programming practice. Global variables introduce tight-coupling between unrelated pieces of code, making them less flexible and vulnerable to unintended side effects. In this case, however, it's okay because you want to generate a tone interactively and then visualize and analyze it later.\n",
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"</div>"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1f81b532-7e0d-4c3b-9c3f-380ab439d8dd",
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"metadata": {},
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"source": [
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"If you choose close frequency values, then you'll hear a peculiar [beating](https://en.wikipedia.org/wiki/Beat_(acoustics)) interference pattern:"
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]
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"execution_count": 3,

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